Question 173690
you have to set this up as 2 different parts of a lonnnnnnnnnggggggg trip.
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lets call the 2nd part of the trips rate r and time t and 
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so then we will call the first part of the trips rate r+5 and the time 8-t(total time minus 2nd part of the trips time(t))
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so
75=rt......................eq 1
60=(r+5)(8-t)..........eq 2
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lets rewrite eq 1 to t=75/r and plug t's value into eq 2
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60=(r+5)(8-(75/r))
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60=(r+5)((8r-75)/r).........now multiply both sides by r
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60r=(r+5)(8r-75)
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{{{60r=8r^2-75r+40r-375}}}
{{{8r^2-95r-375+0}}}
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throw out negative answer{{{system(r=15,r=-3.125)}}}
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therefore rate on 75 mile part of trip is 15mph
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rate on 60 mile part of trip is {{{highlight(r+5=15+5-20)}}}mph 
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 *[invoke solve_quadratic_equation 8, -95, -375]